18.17 : 泊松比、弹性模量和刚性模量之间的关系

A slender bar subjected to an axial load undergoes deformation in the axial and transverse directions. The deformation affects the cubic elements within it.

Depending on its orientation, the cube is transformed into a rectangular parallelepiped or a rhombus, resulting in shearing strain.

The axial loading on the element results in a combination of shearing and normal strains.

Applying an axial load triggers normal and shearing stresses on elements that are oriented at an angle of 45 degrees to the load axis.

The cubic element, when intersected with a diagonal plane, forms a prismatic element. The prismatic element modifies its internal angles and sides in a manner proportional to the strains generated by the load.

By applying the formula for the tangent of the difference of two angles, the relationship between the maximum shearing strain and the axial strain is determined.

From Hooke's law, the relation between the constants is obtained. One constant can be determined from the other two.